Certain nonlinear partially observable stochastic optimal control problems with explicit control laws equivalent to LEQG/LQG problems

IEEE Transactions on Automatic Control

Volumn 42, Issue 4, 1997, Pages 482-497

  Charalambous, Charalambos D ^a   Elliott, Robert J ^b  

^a MCGILL UNIVERSITY   (Canada)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

LEQG; LQG; Nonlinear filtering; Risk sensitive; Separation; Stochastic control

Indexed keywords

COMPUTATIONAL METHODS; CONTROL NONLINEARITIES; CONTROL SYSTEM ANALYSIS; KALMAN FILTERING; MATHEMATICAL MODELS; OBSERVABILITY; STATE ESTIMATION; STATISTICAL METHODS; STOCHASTIC CONTROL SYSTEMS;

LINEAR EXPONENTIAL QUADRATIC GAUSSIAN (LEQG) CONTROL; LINEAR QUADRATIC GAUSSIAN (LQG) CONTROL; RISK SENSITIVE CONTROL SYSTEMS; SEPARATION PRINCIPLE;

OPTIMAL CONTROL SYSTEMS;

EID: 0031116996     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.566658     Document Type: Article

References (23)

1. C. Charalambous and R. J. Elliott, "Classes of nonlinear partially observable stochastic optimal control problems with explicit optimal control laws," SIAM J. Contr. Optimiz., to appear.
2. W. M. Wonham, "On the separation theorem of stochastic control," SIAM J. Contr., vol. 6, no. 2, pp. 312-326, 1968.
3. R. E. Mortensen, "Stochastic optimal control with noisy observations," Int. J. Contr., vol. 4, pp. 455-464, 1966.
4. A. Jazwinski, Stochastic Processes and Filtering Theory. New York: Academic, 1970.
5. V. E. Benes and I. Karatzas, "On the relation of Zakai's and Mortensen's equations," SIAM J. Contr. Optimiz., vol. 21, no. 3, pp. 472-489, 1983.
6. P. Caines, Linear Stochastic Systems. New York: Wiley, 1988.
7. V. Benes, "Exact finite-dimensional filters for certain diffusions with nonlinear drift," Stochastics, vol. 5, pp. 65-92, 1981.
8. Proc. NATO Advanced Study Inst., Stochastic Systems: The Mathematics of Filtering and Identification and Applications, M. Hazewinkel and J. C. Willems, Eds. D. Reidel, 1981.
9. U. Haussmann and E. Pardoux, "A conditionally almost linear filtering problem with non-Gaussian initial condition," Stochastics, vol. 23, pp. 241-275, 1988.
10. A. Bensoussan, Stochastic Control of Partially Observable Systems. Cambridge: Cambridge Univ., 1992.
11. V. Benes and L. Shepp, "Wiener integral associated with diffusion processes," Teoriya Veroiatnostei i Prem., vol. 3, pp. 498-501, 1968.
12. C. Charalambous, D. Naidu, and K. Moore, "Solvable risk-sensitive control problems with output feedback," in Proc. 33rd IEEE Conf. Decision. Contr., Lake Buena Vista, FL, Dec. 1994, pp. 1433-1434.
13. C. Charalambous, "Partially observable nonlinear risk-sensitive control problems: Dynamic programming and verification theorems," IEEE Trans. Automat. Contr., to appear.
14. A. Bensoussan and R. Elliott, "General finite dimensional risk sensitive problems and small noise limits," IEEE Trans. Automat. Contr., vol. 41, no. 2, pp. 210-215, 1996.
15. V. Benes and R. Elliott, "Finite dimensional solutions of a modified Zakai equation," in IFAC Symp. Nonlinear Contr. Syst. Design, Tahoe City, CA, June 1995.
16. R. S. Lipster and A. N. Shiryayev, Statistics of Random Processes, vol. 1. New York: Springer-Verlag, 1977.
17. R. Elliott, Stochastic Calculus and Applications. New York: Springer-Verlag, 1982.
18. C. Charalambous and J. Hibey, "Minimum principle for partially observable nonlinear risk-sensitive control problems using measure-valued decompositions," Stochastics Stochastics Rep., vol. 57, pp. 247-288, 1996.
19. R. W. Brockett and J. M. C. Clark, "The geometry of the conditional density equation," in Proc. Conf. Anal. Optimiz. Stochastic Syst., Oxford, England, 1978.
20. D. Ocone, "Topics in nonlinear filtering," Ph.D. dissertation, M.I.T., 1980.
21. S. Mitter, "On the analogy between mathematical problems of nonlinear filtering and quantum physics," Ricerche di Automat., vol. 10, no. 2, pp. 163-216, 1979.
22. J. S. Baras, G. L. Blankenship, and W. E. Hopkins, "Existence, uniqueness, and asymptotic behavior of solutions to a class of Zakai equations with unbounded coefficients," IEEE Trans. Automat. Contr., vol. 28, no. 2, pp. 203-214, 1983.
23. C. Charalambous, "The role of information state and adjoint in relating nonlinear output feedback risk-sensitive control and dynamic games," IEEE Trans. Automat. Contr., to appear.